The source of a number x is an additional number, which when multiplied by chin a given variety of times, equates to x.

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For example, the third root (also called the cube root) of 64 is 4, due to the fact that if friend multiply 3 fours together you gain 64:
This would certainly be composed as The above would be talked as "the third root the 64 is 4" or "the cube root of 64 is 4".

The 2nd root is usually referred to as the "square root".The third root the a number is usually called the "cube root", after that, castle are referred to as the nth root, for instance the 5th root, 7th root etc

Sometimes there are two roots

For every even-degree source (for example the 2nd, 4th, sixth ....) there space two roots. This is since multiplying two optimistic or two negative numbers both produce a hopeful result. For example, think about the square root of 9.

What number, multiplied by chin will create 9? Obviously 3 will certainly work:
3 × 3 = 9
But so will certainly -3:
-3 × -3 = 9

When there are two roots prefer this, unless declared otherwise we median the positive one. For this reason strictly speaking, when we write √4, we median the confident root, +2. This is referred to as the "principal root".

Roots of an adverse numbers

There space no genuine even-order root of negative numbers. For instance there is no real square root of -9, due to the fact that -3 × -3 =+9, and +3 × +3 =+9 also. This uses to every even-order roots, second (square) root, 4th root, 6th root and so on.

However, there are odd-order root of an adverse numbers. For example –3 is a cube source of –27. This is due to the fact that –3 × –3 × –3 = –27. The very first two terms once multiplied develop +9, then the next multiply is+9 × –3 = –27.This applies to every odd-order roots such as third (cube) root, fifth root 7th source etc.

Imaginary numbers

It states over that over there is no real square source of a negative number. Keep in mind the word "real". What this is saying is the there is no actual numberthat is the square root of a an unfavorable number.

However, in math and engineering we typically have the require to uncover the square source of a negative number. To deal with this, we present the idea of the "imaginary" number. It entails the symbol i which means the square source of negative one. Or put an additional way, i2 = –1

In usage , we deserve to use it come express the square source of any negative number. For example

This means that the square source of –25 is the square source of +25 time the square root of an unfavorable one.

For an ext on imaginary number seeImaginary numbers.

The symbols


The thing you room finding the root of.

Radical symbol

The √
price that way "root of". The size of the horizontal bar is important. See keep in mind below.


The variety of times the radicand is multiplied by itself. 2 method square root, 3 way cube root.After that they are called the 4th root, 5th root and so on.If this is missing, the is presume to be 2 - the square root.

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Another means to create it

Roots can also be written in exponent form. In basic So for instance the cube root of x would be writtenWhich would certainly be express "x come the power of one third".